00:01
So here we have a solo model with a production function that is k to the 0 .5, n to the 0 .5, so a, to get the per worker, we just divide by n, right? you get y over n, which is usually denoted little y would be k to the 0 .5 over n to the 0 .5, divided in by n, which is equal to k to the 0 .5 over n to the 0 .5 over n to the 0 .5 is equal to k to the 0 .5 .5.
00:30
We usually use little k for capital per worker.
00:33
So now income per worker is a function of capital per worker.
00:37
We also know a few other things, right, turning to b.
00:40
We're told that the savings rate is 0 .1.
00:43
We're told that the population growth rate is equal to 0 .02.
00:47
And we're told that the depreciation rate d is equal to 0 .03, right? so we want, oh, this is still a.
00:56
We want to find the per capita output.
01:00
Well, what does equilibrium look like, right? equilibrium in the solar model is when usually you write it as s, y, that savings per worker, is equal to n plus dk, right? that's the draw on capital per worker.
01:17
So this would give us s, k to 0 .5, is equal to n plus delta k.
01:24
And that's going to tell me that k to the 0 .5 is equal to s over n plus delta.
01:33
And that means that k is equal to 0 .1 over 0 .05, all squared, which is equal to 2 squared, which is equal to 4, which would be capital per worker.
01:45
And that means that output per worker is k to the 0 .5 is equal to equal to 4 to 0 .5 is equal to 2.
01:56
So we've got very nice values for k and per capita output.
02:00
The golden rule here is we need to remember...